Based on the bi-material triangle lattice material, a new cellular structure: bi-material re-entrant triangle (BRT) is devised to incorporate tailorable coefficient of thermal expansion (CTE) and tunable Poisson’s ratio (PR) properties by replacing the straight base of a triangle with two hypotenuse members. An equation to systematically build the relationship among the external force, the temperature increment and the deformation for the planar lattice material with bounded joints is derived and then embedded into a theoretical model for devised BRT structure. Using master stiffness equation, effective PR, effective Young’s modulus as well as effective CTE are computed. In order to guide designers to construct an initial concept quickly, the design domain for coupling negative CTE and negative PR properties is proposed. Nine available paired characteristics for coupling effect are extracted and demonstrated with ABAQUS simulation.